{"paper":{"title":"Maximum-Weight Two Boxes Symmetric Difference Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Carlos Seara, Jos\\'e Fern\\'andez Goycoolea, Luis H. Herrera, Pablo P\\'erez Lantero","submitted_at":"2026-05-21T16:35:13Z","abstract_excerpt":"Let $P$ be a set of $n$ points in the plane, where each element of $P$ is assigned a weight $\\omega(p)$, positive or negative. In this paper, we present an algorithm that runs in $O(n^4\\log n)$ time and $O(n)$ space to find two possibly overlapping axis-aligned rectangles $A$ and $B$ so as to maximize the total weight of the points contained in the symmetric difference of $A$ and $B$. The same optimization framework can easily be adapted to solve related problems such as to maximize the total weight in the symmetric difference of $k \\geq 3$ boxes and/or in the union of $k \\geq 2$ boxes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22690","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22690/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}